Computer Algebra and Symbolic Computation: Elementary Algorithms
This is the first volume of a two-volume introduction to symbolic computation. The first volume tries to bridge the gap between software manuals that only explain how to use computer algebra programs such as Mathematica or Maple, and graduate texts which only describe algorithms. It is aimed at undergraduate students of mathematics, computer science and engineering. The mathematical prerequisites are the usual undergraduate two-year course of mathematical analysis, elementary linear algebra and applied ordinary differential equations. The computer science prerequisites are experience with a computer programming language and the skills in problem-solving and algorithm development from a beginning programming course. The presentation is based on an algorithmic language called mathematical pseudolanguage (MPL).
After introducing the language in Chapter 2, the author investigates the internal tree structure of mathematical expressions in Chapter 3. Chapter 4 contains description of elementary algorithms, while Chapter 5 deals with recursion as a programming technique and gives a number of examples that illustrate its advantages and limitations. Chapter 6 is concerned with algorithms that analyse and manipulate polynomials and rational expressions. The final chapter deals with algorithms manipulating exponential and trigonometric functions. The book comes with a CD with the entire text, active hyperlinks, and complete algorithms. It can be recommended to anyone interested in the magic of computer algebra systems.